reserve a,b,c,d for Real;
reserve z,z1,z2 for Complex;

theorem Th59:
  |.z1.| - |.z2.| <= |.z1 - z2.|
proof
  z1 = z1 - z2 + z2;
  then |.z1.| <= |.z1 - z2.| + |.z2.| by Th56;
  hence thesis by XREAL_1:20;
end;
